Sorry but I had never heard that phrased like that before Vacation someplace a little more tropical! LOL!it's still THEIR yard. Sorry, if you came to me I'd tell you sorry, buy an AC unit. And I'm not even a smoker! You said that you put the new addition there and the fan unit because that is the coolest area/best breeze. That's probably why they are smoking there - because it is a cool and comfortable place.
People on this group tend to be very aware of attempts to remove personal freedom. While it doesn't hurt to ask, don't be surprised if the neighbor tells you to vacation someplace a little more tropical.....